Generating minimax-curvature and shorter η<sup>3</sup>-spline path using multi-objective variable-length genetic algorithm

Abstract

As a continuing work on G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> -continuous path planning for nonholonomic wheeled unicycle-type nonholo-nomic mobile robot in the predefined static environment, this paper accounts for a multi-objective path optimization problem that directly incorporates the objectives of simultaneously minimizes the total path length and the maximum curvature along the path. Using easily customized variable-length Island-based Parallel Genetic Algorithm (IPGA) as a path computing framework and η <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> -splines as the path primitive for waypoint interpolation, a multi-objective genetic algorithm is implemented to find and optimize multiple collision-free paths to obtain a G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> -continuous composite η <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> -spline path with each η <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> -spline segment shorter and a larger minimum turning radius along the whole path. By comparing with the corresponding single-objective implementation, the experimental result demonstrates the effectiveness of the evolutionary multi-objective path planner in finding paths of more practical value in complex environments.